Finite Group Databasebeta

← C17×#13390 #16871134

Subgroups — C17×#13390 #16871134

Order 4352.

382 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#473C211yesmaximal, characteristic
2C17×#2161C211yesmaximal, characteristic, complemented
3C2×C17×#362C211yesmaximal, characteristic, complemented
4C2×C17×#362C211yesmaximal, characteristic, complemented
5C17×#2117C211yesmaximal, characteristic
6C17×#1813C211yesmaximal, characteristic
7C17×#1388C211yesmaximal, characteristic, complemented
8C2×C17×#137—21no—
9C22×Q16×C17C2211yescharacteristic
10C2×C17×#131C2211yescharacteristic
11C2×C17×M32C2211yescharacteristic
12C2×C17×M32C2211yescharacteristic
13C17×#473—22no—
14C17×#473—22no—
15C2×C17×#108C2211yescharacteristic
16C2×C17×#108C2211yescharacteristic
17C2×C17×#108C2211yescharacteristic
18C17×#413—21no—
19C2×C17×#101—21no—
20C17×#368—22no—
21C17×#362—22no—
22C17×#362—22no—
23C17×#350—22no—
24C17×#338—21no—
25C2×#41×C17D411yescharacteristic
26C22×Q8×C17—21no—
27C17×#137—24no—
28C17×#137—42no—
29C2×Q16×C17—21no—
30C2×Q16×C17—21no—
31C2×Q16×C17—21no—
32C2×Q16×C17—21no—
33C2×Q16×C17—21no—
34C2×Q16×C17—41no—
35C2×Q16×C17D412yes—
36C2×SD16×C17—41no—
37C17×#131—21no—
38C17×#131—21no—
39C17×#131—21no—
40C17×#131—21no—
41C2×M16×C17—21no—
42C2×M16×C17—21no—
43C2×M16×C17—21no—
44C2×M16×C17—21no—
45C2×M16×C17D411yescharacteristic
46C22×C8×C17—21no—
47C22×C8×C17C2311yescharacteristic
48C17×M32—21no—
49C17×M32—21no—
50C17×M32—21no—
51C17×M32D412yes—
52C2×C16×C17—21no—
53C2×C16×C17—21no—
54C17×#108—21no—
55C17×#108—21no—
56C17×#108—21no—
57C17×#108—21no—
58C17×#108—21no—
59C17×#108D412yes—
60C17×#101—24no—
61C17×#101—41no—
62C17×#100—41no—
63#41×C17—21no—
64#41×C17—21no—
65#41×C17—21no—
66#41×C17—21no—
67C2×Q8×C17—22no—
68C2×Q8×C17—41no—
69C2×Q8×C17—41no—
70C2×Q8×C17—41no—
71C2×Q8×C17—41no—
72C2×Q8×C17—41no—
73C2×Q8×C17D811yescharacteristic
74C2×D4×C17—21no—
75C2×D4×C17D811yescharacteristic
76C22×C4×C17—21no—
77C22×C4×C17—41no—
78C22×C4×C17C2×D411yescharacteristic
79Q16×C17—22no—
80Q16×C17—22no—
81Q16×C17—44no—
82Q16×C17—41no—
83Q16×C17—41no—
84SD16×C17—44no—
85M16×C17—22no—
86M16×C17—21no—
87M16×C17—21no—
88M16×C17—41no—
89M16×C17—41no—
90M16×C17—41no—
91M16×C17—41no—
92M16×C17—41no—
93M16×C17—41no—
94M16×C17—41no—
95C2×C8×C17—21no—
96C2×C8×C17—41no—
97C2×C8×C17—41no—
98C2×C8×C17—41no—
99C2×C8×C17—41no—
100C2×C8×C17—41no—
101C2×C8×C17C2×D411yescharacteristic
102C2×C8×C17C2×D411yescharacteristic
103C2×C8×C17C2×D411yescharacteristic
104C2×C8×C17#4111yescharacteristic
105C2×C8×C17#4111yescharacteristic
106C2×C8×C17#4111yescharacteristic
107C16×C17—22no—
108C16×C17—41no—
109#13390C1711yesmaximal, characteristic, direct product factor, Sylow
110C23×C17—21no—
111C23×C17#13711yescharacteristic
112Q8×C17—21no—
113Q8×C17—21no—
114Q8×C17—42no—
115Q8×C17—42no—
116Q8×C17—81no—
117Q8×C17—81no—
118D4×C17—21no—
119D4×C17—21no—
120D4×C17—41no—
121D4×C17—41no—
122C2×C4×C17—21no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—42no—
126C2×C4×C17—81no—
127C2×C4×C17—81no—
128C2×C4×C17#12011yescharacteristic
129C2×C4×C17#12111yescharacteristic
130C2×C4×C17#12311yescharacteristic
131C2×C4×C17C2×D811yescharacteristic
132C2×C4×C17#13511yescharacteristic
133C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
134C8×C17—41no—
135C8×C17—42no—
136C8×C17—81no—
137C8×C17—81no—
138C8×C17#12111yescharacteristic
139C8×C17#12111yescharacteristic
140C8×C17#12311yescharacteristic
141C8×C17#12411yescharacteristic
142C2×#473C2×C1711yescharacteristic
143#2161C2×C1711yescharacteristic, complemented
144C2×#362C2×C1711yescharacteristic, complemented
145C2×#362C2×C1711yescharacteristic, complemented
146#2117C2×C1711yescharacteristic
147#1813C2×C1711yescharacteristic
148#1388C2×C1711yescharacteristic, complemented
149C22×C17—41no—
150C22×C17—41no—
151C22×C17—81no—
152C22×C17#45211yescharacteristic
153C22×C17#46811yescharacteristic
154C22×C17#48011yescharacteristic
155C4×C17—41no—
156C4×C17—82no—
157C4×C17#39411yescharacteristic
158C4×C17#44711yescharacteristic
159C4×C17#46611yescharacteristic
160C4×C17#48211yescharacteristic
161C2×#137—21no—
162C22×Q16C22×C1711yescharacteristic
163C2×#131C22×C1711yescharacteristic
164C2×M32C22×C1711yescharacteristic
165C2×M32C22×C1711yescharacteristic
166#473—22no—
167#473—22no—
168C2×#108C22×C1711yescharacteristic
169C2×#108C22×C1711yescharacteristic
170C2×#108C22×C1711yescharacteristic
171#413—21no—
172C2×#101—21no—
173#368—22no—
174#362—22no—
175#362—22no—
176#350—22no—
177#338—21no—
178C2×C17—21no—
179C2×C17—21no—
180C2×C17—21no—
181C2×C17—81no—
182C2×C17#203311yescharacteristic
183C2×#41D4×C1711yescharacteristic
184C22×Q8—21no—
185#137—24no—
186#137—42no—
187C2×Q16—21no—
188C2×Q16—21no—
189C2×Q16—21no—
190C2×Q16—21no—
191C2×Q16—21no—
192C2×Q16—41no—
193C2×Q16D4×C1712yes—
194C2×SD16—41no—
195#131—21no—
196#131—21no—
197#131—21no—
198#131—21no—
199C2×M16—21no—
200C2×M16—21no—
201C2×M16—21no—
202C2×M16—21no—
203C2×M16D4×C1711yescharacteristic
204C22×C8—21no—
205C22×C8C23×C1711yescharacteristic
206M32—21no—
207M32—21no—
208M32—21no—
209M32D4×C1712yes—
210C2×C16—21no—
211C2×C16—21no—
212#108—21no—
213#108—21no—
214#108—21no—
215#108—21no—
216#108—21no—
217#108D4×C1712yes—
218#101—24no—
219#101—41no—
220#100—41no—
221C17#1339011yescharacteristic, direct product factor, Sylow
222#41—21no—
223#41—21no—
224#41—21no—
225#41—21no—
226C2×Q8—22no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8D8×C1711yescharacteristic
233C2×D4—21no—
234C2×D4D8×C1711yescharacteristic
235C22×C4—21no—
236C22×C4—41no—
237C22×C4C2×D4×C1711yescharacteristic
238Q16—22no—
239Q16—22no—
240Q16—44no—
241Q16—41no—
242Q16—41no—
243SD16—44no—
244M16—21no—
245M16—22no—
246M16—21no—
247M16—41no—
248M16—41no—
249M16—41no—
250M16—41no—
251M16—41no—
252M16—41no—
253M16—41no—
254C2×C8—21no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8C2×D4×C1711yescharacteristic
261C2×C8C2×D4×C1711yescharacteristic
262C2×C8C2×D4×C1711yescharacteristic
263C2×C8#41×C1711yescharacteristic
264C2×C8#41×C1711yescharacteristic
265C2×C8#41×C1711yescharacteristic
266C16—22no—
267C16—41no—
268C23—21no—
269C23C17×#13711yescharacteristic
270Q8—21no—
271Q8—21no—
272Q8—42no—
273Q8—42no—
274Q8—81no—
275Q8—81no—
276D4—21no—
277D4—21no—
278D4—41no—
279D4—41no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—42no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4C17×#12011yescharacteristic
287C2×C4C17×#12111yescharacteristic
288C2×C4C17×#12311yescharacteristic
289C2×C4C2×D8×C1711yescharacteristic
290C2×C4C17×#13511yescharacteristic
291C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
292C8—41no—
293C8—42no—
294C8—81no—
295C8—81no—
296C8C17×#12111yescharacteristic
297C8C17×#12111yescharacteristic
298C8C17×#12311yescharacteristic
299C8C17×#12411yescharacteristic
300C22—41no—
301C22—41no—
302C22—81no—
303C22C17×#45211yescharacteristic
304C22C17×#46811yescharacteristic
305C22C17×#48011yescharacteristic
306C4—41no—
307C4—82no—
308C4C17×#39411yescharacteristic
309C4C17×#44711yescharacteristic
310C4C17×#46611yescharacteristic
311C4C17×#48211yescharacteristic
312C2—21no—
313C2—21no—
314C2—21no—
315C2—81no—
316C2C17×#203311yescharacteristic
subgroupG/H
center, socleC2×C17#2033
commutator, Frattini, cosocleC22×C8C23×C17
prime radicalC2×#41×C17D4
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C17×#2161C2semidirect
3. C2×C17×#362C2semidirect
4. C2×C17×#362C2semidirect
7. C17×#1388C2semidirect
109. #13390C17direct (N × H)
143. #2161C2×C17semidirect
144. C2×#362C2×C17semidirect
145. C2×#362C2×C17semidirect
148. #1388C2×C17semidirect
221. C17#13390direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C17×#4732
C17×#21612
C2×C17×#3622
C17×#21172
C17×#18132
C17×#13882
#1339017